Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Local control of bias and tension in beta-splines
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
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We describe a new type of parametrically defined space curve. The parameters which define these curves allow for the convenient control over local shape attributes while maintaining global second order geometric continuity. The coordinate functions are defined by piecewise segments of rational functions, each segment being the ratio of cubic polynomials and a common quadratic polynomial. Each curve segment is a planar curve and where two segments meet the curvature is zero. This simple mathematical representation permits these curves to be efficiently manipulated and displayed.